# Notes¶

In the core-shell potential [DO58], ions are modelled as two particles: A core and a massless shell which share the ion charge. As the shells are massless they will instantaneously move to positions such that the forces on the shells are zero. This is achieved by optimizing the potential energy with respect to the shell positions. The cores and the corresponding shells are connected by bonded potentials.

In the CoreShellHarmonicPotential, core and shell are connected via a harmonic potential:

$E^\mathrm{core-shell}(r_\mathrm{core-shell}) = \frac{1}{2} K (r_\mathrm{core-shell} - r_0)^2 \, .$

The CoreShellMorsePotential, defines a MorsePotential:

$E^\mathrm{core-shell}(r_\mathrm{core-shell}) = E_0 \left ( \left [ 1 - e^{k(r_\mathrm{core-shell} - r_0)} \right ]^2 -1 \right )$

between core and shell.

To define core-shell potentials, one must start with specifying all particles types, i.e. both cores and shells where the shells must have mass 0. The shell particles do not need to be specified in the configuration, as they are added automatically within the TremoloXCalculator.

Additional potentials (e.g. BuckinghamPotential or Coulomb-solvers, such as CoulombDSF) can be specified as usual. Please note that the contributions between a core and its corresponding shell from these potentials are not included in forces, stress, and potential energy.

 [DO58] B. G. Dick and A. W. Overhauser. Theory of the dielectric constants of alkali halide crystals. Phys. Rev., 112:90–103, Oct 1958. doi:10.1103/PhysRev.112.90.